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<div class="title">mat33.h</div>  </div>
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<a href="mat33_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment"> * Copyright (c) 2019, NVIDIA CORPORATION. All rights reserved.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment"> * Permission is hereby granted, free of charge, to any person obtaining a</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment"> * copy of this software and associated documentation files (the &quot;Software&quot;),</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment"> * to deal in the Software without restriction, including without limitation</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment"> * the rights to use, copy, modify, merge, publish, distribute, sublicense,</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment"> * and/or sell copies of the Software, and to permit persons to whom the</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment"> * Software is furnished to do so, subject to the following conditions:</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment"> * The above copyright notice and this permission notice shall be included in</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment"> * all copies or substantial portions of the Software.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment"> * THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment"> * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment"> * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment"> * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment"> * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment"> * DEALINGS IN THE SOFTWARE.</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160; </div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#ifndef __MATRIX_33_H_</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="preprocessor">#define __MATRIX_33_H_</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160; </div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="preprocessor">#include &lt;stdio.h&gt;</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="preprocessor">#include &lt;unistd.h&gt;</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="preprocessor">#include &lt;math.h&gt;</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="logging_8h.html">logging.h</a>&quot;</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160; </div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T1, <span class="keyword">typename</span> T2&gt;</div>
<div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="group__matrix.html#ga2a59a3e770f0f421c2e21df6f86df48f">   38</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga2a59a3e770f0f421c2e21df6f86df48f">mat33_cast</a>( T1 dst[3][3], <span class="keyword">const</span> T2 src[3][3] )</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;{</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        <span class="keywordflow">for</span>( uint32_t i=0; i &lt; 3; i++ )</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;                <span class="keywordflow">for</span>( uint32_t j=0; j &lt; 3; j++ )</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;                        dst[i][j] = (T1)src[i][j];</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;}</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160; </div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160; </div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00051"></a><span class="lineno"><a class="line" href="group__matrix.html#ga4081852912b45ee44f0243ff5718203c">   51</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga4081852912b45ee44f0243ff5718203c">mat33_copy</a>( T dst[3][3], <span class="keyword">const</span> T src[3][3] )</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;{</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        memcpy(dst, src, <span class="keyword">sizeof</span>(T) * 9);</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;}</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="group__matrix.html#ga337284e19938f8654d8ebf6dcf6f257b">   62</a></span>&#160;<span class="keyword">inline</span> T <a class="code" href="group__matrix.html#ga337284e19938f8654d8ebf6dcf6f257b">mat33_det</a>( <span class="keyword">const</span> T src[3][3] )</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;{</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keywordflow">return</span> src[0][0] * (src[1][1] * src[2][2] - src[1][2] * src[2][1])</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;                - src[0][1] * (src[1][0] * src[2][2] - src[1][2] * src[2][0])</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;                + src[0][2] * (src[1][0] * src[2][1] - src[1][1] * src[2][0]);</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;}</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160; </div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="group__matrix.html#ga984ddbe902542e96416bb22c5c824b80">   75</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga984ddbe902542e96416bb22c5c824b80">mat33_identity</a>( T dst[3][3] )</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;{</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        dst[0][0] = 1; dst[0][1] = 0; dst[0][2] = 0;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        dst[1][0] = 0; dst[1][1] = 1; dst[1][2] = 0;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        dst[2][0] = 0; dst[2][1] = 0; dst[2][2] = 1;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;}</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160; </div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00089"></a><span class="lineno"><a class="line" href="group__matrix.html#gab7c879d25c250f9b0bbf43d1ca351a84">   89</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#gab7c879d25c250f9b0bbf43d1ca351a84">mat33_inverse</a>( T dst[3][3], <span class="keyword">const</span> T src[3][3] )</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;{</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        T inv[3][3];</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160; </div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        <span class="comment">// invert</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        <span class="keyword">const</span> T det = <a class="code" href="group__matrix.html#ga337284e19938f8654d8ebf6dcf6f257b">mat33_det</a>(src);</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        inv[0][0] = + (src[1][1] * src[2][2] - src[1][2] * src[2][1]);</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        inv[0][1] = - (src[0][1] * src[2][2] - src[0][2] * src[2][1]);</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        inv[0][2] = + (src[0][1] * src[1][2] - src[0][2] * src[1][1]);</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        inv[1][0] = - (src[1][0] * src[2][2] - src[1][2] * src[2][0]);</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        inv[1][1] = + (src[0][0] * src[2][2] - src[0][2] * src[2][0]);</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        inv[1][2] = - (src[0][0] * src[1][2] - src[0][2] * src[1][0]);</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        inv[2][0] = + (src[1][0] * src[2][1] - src[1][1] * src[2][0]);</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        inv[2][1] = - (src[0][0] * src[2][1] - src[0][1] * src[2][0]);</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        inv[2][2] = + (src[0][0] * src[1][1] - src[0][1] * src[1][0]);</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160; </div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        <span class="comment">// scale by determinant</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        <span class="keywordflow">for</span>( uint32_t i=0; i &lt; 3; i++ )</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                <span class="keywordflow">for</span>( uint32_t k=0; k &lt; 3; k++ )</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                        dst[i][k] = inv[i][k] / det;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;}</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160; </div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160; </div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00118"></a><span class="lineno"><a class="line" href="group__matrix.html#ga17719324015094525794f664c86ba20d">  118</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga17719324015094525794f664c86ba20d">mat33_multiply</a>( T dst[3][3], <span class="keyword">const</span> T a[3][3], <span class="keyword">const</span> T b[3][3] )</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;{</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        T tmp[3][3];</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;        </div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        <span class="keywordflow">for</span>( <span class="keywordtype">int</span> i=0; i &lt; 3; i++ )</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        {</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;                <span class="keywordflow">for</span>( <span class="keywordtype">int</span> j=0; j &lt; 3; j++ )</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;                {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;                        tmp[i][j] = 0;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160; </div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;                        <span class="keywordflow">for</span>( <span class="keywordtype">int</span> k=0; k &lt; 3; k++ )</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                                tmp[i][j] = tmp[i][j] + a[i][k] * b[k][j];</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                }</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;        }</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        </div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;        <a class="code" href="group__matrix.html#ga4081852912b45ee44f0243ff5718203c">mat33_copy</a>(dst, tmp);</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;}</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160; </div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00142"></a><span class="lineno"><a class="line" href="group__matrix.html#ga58d12875af4d112afdc1354e66f488d2">  142</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga58d12875af4d112afdc1354e66f488d2">mat33_print</a>( <span class="keyword">const</span> T src[3][3], <span class="keyword">const</span> <span class="keywordtype">char</span>* name=NULL )</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;{</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        <span class="keywordflow">if</span>( name != NULL )</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;                <a class="code" href="group__log.html#ga228a21f91213b15d7fdce08182d825e8">LogInfo</a>(<span class="stringliteral">&quot;%s = \n&quot;</span>, name);</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160; </div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        printf(<span class="stringliteral">&quot; [ &quot;</span>);</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160; </div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keywordflow">for</span>( uint32_t i=0; i &lt; 3; i++ )</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;        {</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;                <span class="keywordflow">for</span>( uint32_t j=0; j &lt; 3; j++ )</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;                        <a class="code" href="group__log.html#ga228a21f91213b15d7fdce08182d825e8">LogInfo</a>(<span class="stringliteral">&quot;%f &quot;</span>, src[i][j]);</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160; </div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;                <span class="keywordflow">if</span>( i &lt; 2 )</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;                {</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;                        <a class="code" href="group__log.html#ga228a21f91213b15d7fdce08182d825e8">LogInfo</a>(<span class="stringliteral">&quot;\n   &quot;</span>);</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;                }</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;                <span class="keywordflow">else</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;                {</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;                        <a class="code" href="group__log.html#ga228a21f91213b15d7fdce08182d825e8">LogInfo</a>(<span class="stringliteral">&quot;]\n&quot;</span>);</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                }</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        }</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;}</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160; </div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00171"></a><span class="lineno"><a class="line" href="group__matrix.html#gafa786e888812cb8d884c5e585914b609">  171</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code" href="group__matrix.html#gafa786e888812cb8d884c5e585914b609">mat33_rank</a>( <span class="keyword">const</span> T src[3][3] )</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;{</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        T mat[3][3];</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160; </div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;        <span class="comment">// reducing to row-echelon form alters the matrix</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;        <a class="code" href="group__matrix.html#ga4081852912b45ee44f0243ff5718203c">mat33_copy</a>(mat, src);</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160; </div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;        <span class="comment">// iteratively compute the rank</span></div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;        <span class="keywordtype">int</span> rank = 3;   <span class="comment">// (= #columns)</span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;  </div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;        <span class="keywordflow">for</span>( <span class="keywordtype">int</span> row=0; row &lt; rank; row++ ) </div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;        { </div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;                <span class="keywordflow">if</span>( mat[row][row] != 0 ) </div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;                { </div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;                        <span class="keywordflow">for</span>( <span class="keywordtype">int</span> col=0; col &lt; 3; col++ ) </div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;                        { </div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;                                <span class="keywordflow">if</span> (col != row) </div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;                                { </div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;                                        <span class="keyword">const</span> T mult = mat[col][row] / mat[row][row]; </div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160; </div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;                                        <span class="keywordflow">for</span>( <span class="keywordtype">int</span> i = 0; i &lt; rank; i++ ) </div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;                                                mat[col][i] -= mult * mat[row][i]; </div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;                                } </div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;                        } </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;                } </div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;                <span class="keywordflow">else</span></div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;                { </div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;                        <span class="keywordtype">bool</span> reduce = <span class="keyword">true</span>; </div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160; </div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;                        <span class="keywordflow">for</span>( <span class="keywordtype">int</span> i=row+1; i &lt; 3; i++ ) </div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;                        { </div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                                <span class="keywordflow">if</span>( mat[i][row] != 0 ) </div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;                                {</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;                                        <span class="keywordflow">for</span>( <span class="keywordtype">int</span> k=0; k &lt; rank; k++ )</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;                                        {</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;                                                <span class="keyword">const</span> T tmp = mat[row][k];</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;                                                mat[row][k] = mat[i][k];</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;                                                mat[i][k] = tmp;</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;                                        }</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160; </div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;                                        reduce = <span class="keyword">false</span>; </div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;                                        break ; </div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;                                } </div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;                        } </div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;  </div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;                        <span class="keywordflow">if</span>( reduce ) </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;                        { </div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;                                rank--; </div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  </div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;                                <span class="keywordflow">for</span>( <span class="keywordtype">int</span> i=0; i &lt; 3; i++ ) </div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;                                        mat[i][row] = mat[i][rank]; </div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;                        } </div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  </div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;                        row--; </div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;                } </div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;        }</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160; </div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;        <span class="keywordflow">return</span> rank; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;}</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160; </div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160; </div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="group__matrix.html#gafc607b02cc864b8571d5a984bc3f1851">  237</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#gafc607b02cc864b8571d5a984bc3f1851">mat33_translate</a>( T dst[3][3], T x, T y )</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;{</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;        <a class="code" href="group__matrix.html#ga984ddbe902542e96416bb22c5c824b80">mat33_identity</a>(dst);</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160; </div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;        dst[0][2] = x;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        dst[1][2] = y;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;}</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160; </div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160; </div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00251"></a><span class="lineno"><a class="line" href="group__matrix.html#ga4a69500377a2f20ff8ca8d269d234c27">  251</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#gafc607b02cc864b8571d5a984bc3f1851">mat33_translate</a>( T dst[3][3], T src[3][3], T x, T y )</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;{</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;        T m[3][3];</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160; </div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;        <a class="code" href="group__matrix.html#gafc607b02cc864b8571d5a984bc3f1851">mat33_translate</a>(m, x, y);</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;        <a class="code" href="group__matrix.html#ga17719324015094525794f664c86ba20d">mat33_multiply</a>(dst, src, m);</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;}</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160; </div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160; </div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00265"></a><span class="lineno"><a class="line" href="group__matrix.html#ga2811064b0130de6dbdb1549e09da0658">  265</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga2811064b0130de6dbdb1549e09da0658">mat33_rotation</a>( T dst[3][3], T degrees )</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;{</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;        <a class="code" href="group__matrix.html#ga984ddbe902542e96416bb22c5c824b80">mat33_identity</a>(dst);</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160; </div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;        <span class="keyword">const</span> T rad = 0.01745329251 * degrees;</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160; </div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;        <span class="keyword">const</span> T c = cos(rad);</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;        <span class="keyword">const</span> T s = sin(rad);</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160; </div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;        dst[0][0] = c;</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;        dst[0][1] = -s;</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;        dst[1][0] = s;</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;        dst[1][1] = c;</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;}</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160; </div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160; </div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00286"></a><span class="lineno"><a class="line" href="group__matrix.html#ga538c44222723e66a248894a05b607523">  286</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga2811064b0130de6dbdb1549e09da0658">mat33_rotation</a>( T dst[3][3], T src[3][3], T degrees )</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;{</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;        T m[3][3];</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160; </div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;        <a class="code" href="group__matrix.html#ga2811064b0130de6dbdb1549e09da0658">mat33_rotation</a>(m, degrees);</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;        <a class="code" href="group__matrix.html#ga17719324015094525794f664c86ba20d">mat33_multiply</a>(dst, src, m);</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;}</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160; </div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160; </div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00300"></a><span class="lineno"><a class="line" href="group__matrix.html#ga8dc86df63cc91d8ef54795775bc53464">  300</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga2811064b0130de6dbdb1549e09da0658">mat33_rotation</a>( T dst[3][3], T degrees, <span class="keywordtype">float</span> origin_x, <span class="keywordtype">float</span> origin_y )</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;{</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;        <a class="code" href="group__matrix.html#gafc607b02cc864b8571d5a984bc3f1851">mat33_translate</a>(dst, origin_x, origin_y);</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;        <a class="code" href="group__matrix.html#ga2811064b0130de6dbdb1549e09da0658">mat33_rotation</a>(dst, dst, degrees);</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;        <a class="code" href="group__matrix.html#gafc607b02cc864b8571d5a984bc3f1851">mat33_translate</a>(dst, dst, -origin_x, -origin_y);</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;}</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160; </div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160; </div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00313"></a><span class="lineno"><a class="line" href="group__matrix.html#gae6097459d236ea6169d737103e2db3e6">  313</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga2811064b0130de6dbdb1549e09da0658">mat33_rotation</a>( T dst[3][3], T src[3][3], T degrees, <span class="keywordtype">float</span> origin_x, <span class="keywordtype">float</span> origin_y )</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;{</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;        <a class="code" href="group__matrix.html#gafc607b02cc864b8571d5a984bc3f1851">mat33_translate</a>(dst, src, origin_x, origin_y);</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;        <a class="code" href="group__matrix.html#ga2811064b0130de6dbdb1549e09da0658">mat33_rotation</a>(dst, dst, degrees);</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;        <a class="code" href="group__matrix.html#gafc607b02cc864b8571d5a984bc3f1851">mat33_translate</a>(dst, dst, -origin_x, -origin_y);</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;}</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160; </div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160; </div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00326"></a><span class="lineno"><a class="line" href="group__matrix.html#ga00f088c37cb0ec42cea53fa7794457e3">  326</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga00f088c37cb0ec42cea53fa7794457e3">mat33_scale</a>( T dst[3][3], T sx, T sy )</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;{</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;        <a class="code" href="group__matrix.html#ga984ddbe902542e96416bb22c5c824b80">mat33_identity</a>(dst);</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160; </div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;        dst[0][0] = sx;</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;        dst[1][1] = sy;</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;}</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160; </div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160; </div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00340"></a><span class="lineno"><a class="line" href="group__matrix.html#ga312e1174aa897fcf54da86ad85193398">  340</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga00f088c37cb0ec42cea53fa7794457e3">mat33_scale</a>( T dst[3][3], T src[3][3], T sx, T sy )</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;{</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;        T m[3][3];</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160; </div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;        <a class="code" href="group__matrix.html#ga00f088c37cb0ec42cea53fa7794457e3">mat33_scale</a>(m, sx, sy);</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;        <a class="code" href="group__matrix.html#ga17719324015094525794f664c86ba20d">mat33_multiply</a>(dst, src, m);</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;}</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160; </div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160; </div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00354"></a><span class="lineno"><a class="line" href="group__matrix.html#ga389b2d87bdb9ab09c3d873a6dcbf2e87">  354</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga389b2d87bdb9ab09c3d873a6dcbf2e87">mat33_shear</a>( T dst[3][3], T sx, T sy )</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;{</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;        <a class="code" href="group__matrix.html#ga984ddbe902542e96416bb22c5c824b80">mat33_identity</a>(dst);</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160; </div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;        dst[0][1] = sx;</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;        dst[1][0] = sy;</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;}</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160; </div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160; </div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00368"></a><span class="lineno"><a class="line" href="group__matrix.html#ga6d183e8a21c5a0035c852ca4d0ebfb15">  368</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga389b2d87bdb9ab09c3d873a6dcbf2e87">mat33_shear</a>( T dst[3][3], T src[3][3], T sx, T sy )</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;{</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;        T m[3][3];</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160; </div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;        <a class="code" href="group__matrix.html#ga389b2d87bdb9ab09c3d873a6dcbf2e87">mat33_shear</a>(m, sx, sy);</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;        <a class="code" href="group__matrix.html#ga17719324015094525794f664c86ba20d">mat33_multiply</a>(dst, src, m);</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;}</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160; </div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160; </div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00382"></a><span class="lineno"><a class="line" href="group__matrix.html#ga14a2f030b3997bbf73afa1b9868534ec">  382</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga14a2f030b3997bbf73afa1b9868534ec">mat33_swap</a>( T a[3][3], T b[3][3] )</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;{</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;        T c[3][3];</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160; </div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;        <a class="code" href="group__matrix.html#ga4081852912b45ee44f0243ff5718203c">mat33_copy</a>(c, a);</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;        <a class="code" href="group__matrix.html#ga4081852912b45ee44f0243ff5718203c">mat33_copy</a>(a, b);</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;        <a class="code" href="group__matrix.html#ga4081852912b45ee44f0243ff5718203c">mat33_copy</a>(b, c);</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;}</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160; </div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160; </div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00397"></a><span class="lineno"><a class="line" href="group__matrix.html#ga494f9ef8df9d1e14afce204581247fa4">  397</a></span>&#160;<span class="keyword">inline</span> T <a class="code" href="group__matrix.html#ga494f9ef8df9d1e14afce204581247fa4">mat33_trace</a>( <span class="keyword">const</span> T src[3][3] )</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;{</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;        <span class="keywordflow">return</span> src[0][0] + src[1][1] + src[2][2];</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;}</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160; </div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160; </div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00408"></a><span class="lineno"><a class="line" href="group__matrix.html#ga04d1860e5b931f43cb60c78ef6dfc464">  408</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga04d1860e5b931f43cb60c78ef6dfc464">mat33_transform</a>( T&amp; x_out, T&amp; y_out, <span class="keyword">const</span> T x_in, <span class="keyword">const</span> T y_in, <span class="keyword">const</span> T mat[3][3] )</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;{</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;        <span class="keyword">const</span> T x = mat[0][0] * x_in + mat[0][1] * y_in + mat[0][2];</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;        <span class="keyword">const</span> T y = mat[1][0] * x_in + mat[1][1] * y_in + mat[1][2];</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;        <span class="keyword">const</span> T z = mat[2][0] * x_in + mat[2][1] * y_in + mat[2][2];</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160; </div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;        x_out = x / z;</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;        y_out = y / z;</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;}</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160; </div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160; </div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00424"></a><span class="lineno"><a class="line" href="group__matrix.html#ga847b97f26a57cbf90f0f1cd3236eadc2">  424</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga04d1860e5b931f43cb60c78ef6dfc464">mat33_transform</a>( T dst[2], <span class="keyword">const</span> T src[2], <span class="keyword">const</span> T mat[3][3] )</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;{</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;        <a class="code" href="group__matrix.html#ga04d1860e5b931f43cb60c78ef6dfc464">mat33_transform</a>(dst[0], dst[1], src[0], src[1], mat);</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;}</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160; </div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160; </div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00435"></a><span class="lineno"><a class="line" href="group__matrix.html#ga3cd7f8bbd5028eb6a4c6fa3f1e83cbe0">  435</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#ga04d1860e5b931f43cb60c78ef6dfc464">mat33_transform</a>( T* dst, <span class="keyword">const</span> T* src, <span class="keyword">const</span> <span class="keywordtype">int</span> N, <span class="keyword">const</span> T mat[3][3] )</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;{</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;        <span class="keywordflow">for</span>( uint32_t n=0; n &lt; N; n++ )</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;                <a class="code" href="group__matrix.html#ga04d1860e5b931f43cb60c78ef6dfc464">mat33_transform</a>(dst[n*2], dst[n*2+1], src[n*2], src[n*2+1], mat); </div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;}</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160; </div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00446"></a><span class="lineno"><a class="line" href="group__matrix.html#gaef64fca8bb6b4a04d2b7497551719c08">  446</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#gaef64fca8bb6b4a04d2b7497551719c08">mat33_transpose</a>( T dst[3][3], <span class="keyword">const</span> T src[3][3] )</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;{</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;        T tmp[3][3];</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;        </div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;        <span class="keywordflow">for</span>( uint32_t i=0; i &lt; 3; i++ )</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;                <span class="keywordflow">for</span>( uint32_t j=0; j &lt; 3; j++ )</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;                        tmp[i][j] = src[j][i];</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;                </div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;        <a class="code" href="group__matrix.html#ga4081852912b45ee44f0243ff5718203c">mat33_copy</a>(dst, tmp);</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;}</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160; </div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160; </div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00463"></a><span class="lineno"><a class="line" href="group__matrix.html#gaf896d4d3e9b5019d367d9f3707305083">  463</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group__matrix.html#gaf896d4d3e9b5019d367d9f3707305083">mat33_zero</a>( T dst[3][3] )</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;{</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;        memset(dst, 0, <span class="keyword">sizeof</span>(T) * 9);</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;}</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160; </div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160; </div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160; </div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<div class="ttc" id="agroup__matrix_html_gab7c879d25c250f9b0bbf43d1ca351a84"><div class="ttname"><a href="group__matrix.html#gab7c879d25c250f9b0bbf43d1ca351a84">mat33_inverse</a></div><div class="ttdeci">void mat33_inverse(T dst[3][3], const T src[3][3])</div><div class="ttdoc">Compute the inverse of a 3x3 matrix, dst=src^-1 It is safe to have dst and src be the same memory.</div><div class="ttdef"><b>Definition:</b> mat33.h:89</div></div>
<div class="ttc" id="agroup__log_html_ga228a21f91213b15d7fdce08182d825e8"><div class="ttname"><a href="group__log.html#ga228a21f91213b15d7fdce08182d825e8">LogInfo</a></div><div class="ttdeci">#define LogInfo(format, args...)</div><div class="ttdoc">Log a printf-style info message (Log::INFO)</div><div class="ttdef"><b>Definition:</b> logging.h:168</div></div>
<div class="ttc" id="agroup__matrix_html_ga2a59a3e770f0f421c2e21df6f86df48f"><div class="ttname"><a href="group__matrix.html#ga2a59a3e770f0f421c2e21df6f86df48f">mat33_cast</a></div><div class="ttdeci">void mat33_cast(T1 dst[3][3], const T2 src[3][3])</div><div class="ttdoc">Cast a 3x3 matrix from one type to another.</div><div class="ttdef"><b>Definition:</b> mat33.h:38</div></div>
<div class="ttc" id="agroup__matrix_html_ga04d1860e5b931f43cb60c78ef6dfc464"><div class="ttname"><a href="group__matrix.html#ga04d1860e5b931f43cb60c78ef6dfc464">mat33_transform</a></div><div class="ttdeci">void mat33_transform(T &amp;x_out, T &amp;y_out, const T x_in, const T y_in, const T mat[3][3])</div><div class="ttdoc">Transform a 2D vector by a 3x3 matrix.</div><div class="ttdef"><b>Definition:</b> mat33.h:408</div></div>
<div class="ttc" id="agroup__matrix_html_ga00f088c37cb0ec42cea53fa7794457e3"><div class="ttname"><a href="group__matrix.html#ga00f088c37cb0ec42cea53fa7794457e3">mat33_scale</a></div><div class="ttdeci">void mat33_scale(T dst[3][3], T sx, T sy)</div><div class="ttdoc">Initialize a 3x3 scaling matrix.</div><div class="ttdef"><b>Definition:</b> mat33.h:326</div></div>
<div class="ttc" id="agroup__matrix_html_ga58d12875af4d112afdc1354e66f488d2"><div class="ttname"><a href="group__matrix.html#ga58d12875af4d112afdc1354e66f488d2">mat33_print</a></div><div class="ttdeci">void mat33_print(const T src[3][3], const char *name=NULL)</div><div class="ttdoc">Print out a 3x3 matrix to stdout.</div><div class="ttdef"><b>Definition:</b> mat33.h:142</div></div>
<div class="ttc" id="agroup__matrix_html_gafa786e888812cb8d884c5e585914b609"><div class="ttname"><a href="group__matrix.html#gafa786e888812cb8d884c5e585914b609">mat33_rank</a></div><div class="ttdeci">int mat33_rank(const T src[3][3])</div><div class="ttdoc">Determine the rank of a 3x3 matrix.</div><div class="ttdef"><b>Definition:</b> mat33.h:171</div></div>
<div class="ttc" id="agroup__matrix_html_ga389b2d87bdb9ab09c3d873a6dcbf2e87"><div class="ttname"><a href="group__matrix.html#ga389b2d87bdb9ab09c3d873a6dcbf2e87">mat33_shear</a></div><div class="ttdeci">void mat33_shear(T dst[3][3], T sx, T sy)</div><div class="ttdoc">Initialize a 3x3 shear matrix.</div><div class="ttdef"><b>Definition:</b> mat33.h:354</div></div>
<div class="ttc" id="agroup__matrix_html_ga494f9ef8df9d1e14afce204581247fa4"><div class="ttname"><a href="group__matrix.html#ga494f9ef8df9d1e14afce204581247fa4">mat33_trace</a></div><div class="ttdeci">T mat33_trace(const T src[3][3])</div><div class="ttdoc">Compute the trace of a 3x3 matrix, returns tr(src)</div><div class="ttdef"><b>Definition:</b> mat33.h:397</div></div>
<div class="ttc" id="agroup__matrix_html_gaf896d4d3e9b5019d367d9f3707305083"><div class="ttname"><a href="group__matrix.html#gaf896d4d3e9b5019d367d9f3707305083">mat33_zero</a></div><div class="ttdeci">void mat33_zero(T dst[3][3])</div><div class="ttdoc">Set a 3x3 matrix to all zero's.</div><div class="ttdef"><b>Definition:</b> mat33.h:463</div></div>
<div class="ttc" id="agroup__matrix_html_ga337284e19938f8654d8ebf6dcf6f257b"><div class="ttname"><a href="group__matrix.html#ga337284e19938f8654d8ebf6dcf6f257b">mat33_det</a></div><div class="ttdeci">T mat33_det(const T src[3][3])</div><div class="ttdoc">Compute the determinant of a 3x3 matrix, returns |src|</div><div class="ttdef"><b>Definition:</b> mat33.h:62</div></div>
<div class="ttc" id="alogging_8h_html"><div class="ttname"><a href="logging_8h.html">logging.h</a></div></div>
<div class="ttc" id="agroup__matrix_html_ga14a2f030b3997bbf73afa1b9868534ec"><div class="ttname"><a href="group__matrix.html#ga14a2f030b3997bbf73afa1b9868534ec">mat33_swap</a></div><div class="ttdeci">void mat33_swap(T a[3][3], T b[3][3])</div><div class="ttdoc">Swap two 3x3 matrices inline, a=b and b=a</div><div class="ttdef"><b>Definition:</b> mat33.h:382</div></div>
<div class="ttc" id="agroup__matrix_html_ga17719324015094525794f664c86ba20d"><div class="ttname"><a href="group__matrix.html#ga17719324015094525794f664c86ba20d">mat33_multiply</a></div><div class="ttdeci">void mat33_multiply(T dst[3][3], const T a[3][3], const T b[3][3])</div><div class="ttdoc">Multiply two 3x3 matrices, dst=a*b</div><div class="ttdef"><b>Definition:</b> mat33.h:118</div></div>
<div class="ttc" id="agroup__matrix_html_ga2811064b0130de6dbdb1549e09da0658"><div class="ttname"><a href="group__matrix.html#ga2811064b0130de6dbdb1549e09da0658">mat33_rotation</a></div><div class="ttdeci">void mat33_rotation(T dst[3][3], T degrees)</div><div class="ttdoc">Initialize a 3x3 rotation matrix.</div><div class="ttdef"><b>Definition:</b> mat33.h:265</div></div>
<div class="ttc" id="agroup__matrix_html_ga984ddbe902542e96416bb22c5c824b80"><div class="ttname"><a href="group__matrix.html#ga984ddbe902542e96416bb22c5c824b80">mat33_identity</a></div><div class="ttdeci">void mat33_identity(T dst[3][3])</div><div class="ttdoc">Initialize a 3x3 identity matrix.</div><div class="ttdef"><b>Definition:</b> mat33.h:75</div></div>
<div class="ttc" id="agroup__matrix_html_ga4081852912b45ee44f0243ff5718203c"><div class="ttname"><a href="group__matrix.html#ga4081852912b45ee44f0243ff5718203c">mat33_copy</a></div><div class="ttdeci">void mat33_copy(T dst[3][3], const T src[3][3])</div><div class="ttdoc">Copy src input matrix to dst output.</div><div class="ttdef"><b>Definition:</b> mat33.h:51</div></div>
<div class="ttc" id="agroup__matrix_html_gafc607b02cc864b8571d5a984bc3f1851"><div class="ttname"><a href="group__matrix.html#gafc607b02cc864b8571d5a984bc3f1851">mat33_translate</a></div><div class="ttdeci">void mat33_translate(T dst[3][3], T x, T y)</div><div class="ttdoc">Initialize a 3x3 translation matrix.</div><div class="ttdef"><b>Definition:</b> mat33.h:237</div></div>
<div class="ttc" id="agroup__matrix_html_gaef64fca8bb6b4a04d2b7497551719c08"><div class="ttname"><a href="group__matrix.html#gaef64fca8bb6b4a04d2b7497551719c08">mat33_transpose</a></div><div class="ttdeci">void mat33_transpose(T dst[3][3], const T src[3][3])</div><div class="ttdoc">Transpose a 3x3 matrix, dst=src^T</div><div class="ttdef"><b>Definition:</b> mat33.h:446</div></div>
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